INGEBRETSON-DISSERTATION-2018.pdf (2.63 MB)
Hausdorff Dimension of Kuperberg Minimal Sets
thesis
posted on 2018-11-27, 00:00 authored by Daniel IngebretsonIn 1994, Kuperberg constructed a smooth flow on a three-manifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minimal set. We develop new techniques to study the symbolic dynamics and dimension theory of this minimal set, by relating it to the limit set of a graph directed pseudo-Markov system over a countable alphabet.
History
Advisor
Hurder, SteveChair
Hurder, SteveDepartment
Mathematics, Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral